One meter of iron, velocity .999c

Quick guesstimate - billions of years, possibly never

http://en.wikipedia.org/wiki/Electromagnetic_projectile_devices_(fiction)
http://en.wikipedia.org/wiki/Mass_driver
http://en.wikipedia.org/wiki/Railgun

BillPatt said:

I'd just like to guesstimate how many lightyears that takes.

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The lightyear is a measure of distance, not time.

I wouldn't be surprised if it collected additional matter.

The lightyear is a measure of distance, not time

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yes, he's asking how far it would travel before it is 'spent.'

I don't know.

She's fast enough for you, old man.

The resulting iron vapor cloud wouldn't be much of a threat to earth, in my opinion. First, it would spread out rapidly rather than staying together. Second, it would be slowed by other forces, including gravity. Third, each iron particle or atom, would have very little momentum and would be quickly stopped by the atomosphere.

BillPatt said:

Given average interstellar density of hydrogen, how long before a one meter sphere of iron

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Iron density is 7870kg/m^3. I assume you mean one meter diameter. Volume = 4/3 pi * (0.5^3) = .524
7870kg/m^3 * .524m^3 = 4123kg = (for those knuckle draggers in the USA) 17,350 lbs. I suppose getting that thing to travel at relativistic velocity is left as an exercise for the reader.

BillPatt said:

travelling at relativistic velocity erodes away?

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I'm not convinced it would simply 'erode.' My SWAG is it would eventually melt, split into smaller liquid bits and then those would eventually vaporize, finally slowing down to not-quite-so-relativistic speeds.

One thing that's going to happen, every hydrogen atom, or God forbid, every larger atom or collection of atoms that hits this thing is going to provide kinetic energy that goes into it and heats it up. I'm assuming the hydrogen atom will be trapped within the sphere (that makes for 100 percent energy transfer into the sphere, making for easier calculation), but at that speed it may well go through, and maybe even take bits of iron nuclei with it.

At rest in empty space the temperature will stabilize at the 3k background radiation, and you can (ignoring heat lost to radiation, which would become significant over time) calculate the temperature rise from there using the energy input and the specific heat of iron. The total input per unit time is of course the number of hydrogen atoms in interstellar space within a cylinder that's the cross-section path of this thing that it travels through in that time.

For the energy of each strike you would calculate the kinetic energy of a hydrogen atom at .999c. With the Lorentz transformations it would be hundreds or maybe thousands of times the kinetic energy as calculated using Newtonian mechanics. At that speed I don't think it would make much difference (again, this is just my SWAG) if its an ordinary-matter hydrogen atom or an antimatter hydrogen atom, as the kinetic energy is so large.

BillPatt said:

Why?

Ever notice one of the standard weapons in interstellar war is the railgun, firing a stream of iron spheres really close to the speed of light?

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Geez, I'm not up on my space opera, but I wonder what the heck that railgun is tied down to. Its design and where it gets that amount of energy are also intriguing questions (Perhaps it's powered by a nuckear explosion, something like the SDI's X-ray Laser), but for this post I'll put those on the back burner.

The reaction force would be huge. I could imagine it being mounted on the Moon and that firing it (especially thousands or millions of times in the same general direction) could cause a measurable change in the Moon's orbit. You couldn't fire this from a smaller platform unless you don't care where or how fast the platform ends up going.

BillPatt said:

Not many contact something like a spaceship. So, what happens to the spent ammo, littering the universe? Eventually, the interstellar medium erodes it away, I'd just like to guesstimate how many lightyears that takes.

Think: as the iron is ablated off, it forms a fast-moving nebula of iron vapor. As each cannonball is in turn ablated, you can get a pretty decent wavefront of fast-moving iron vapor. It's too bad that Earth can be in the way of this.

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I have to wonder how much will still be iron. The hydrogen atom is likely to be stopped or slowed down by hitting an iron nucleus, which will likely split into smaller elements, and perhaps knocking out particles at speeds high enough to split other iron nuclei (any particle physicist should be able to tell you better what will happen). This thing could end up as a soup of atoms below iron on the periodic table. And some nuclei might even fuse, making atoms heavier than iron as well.

ETA: Would something "reasonable" like 0.1 or 0.2c be fast enough?

benbradley said:

Iron density is 7870kg/m^3. I assume you mean one meter diameter. Volume = 4/3 pi * (0.5^3) = .524
7870kg/m^3 * .524m^3 = 4123kg = (for those knuckle draggers in the USA) 17,350 lbs. I suppose getting that thing to travel at relativistic velocity is left as an exercise for the reader.

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If it would weigh 4123 kg, then it would weigh 9087.09 lb. I didn't bother doing the calculations, but I did assume that "one meter" meant one cubic meter, which would mean that it would weigh 7870 kg or 17345.48 lb.

I'm not convinced it would simply 'erode.' My SWAG is it would eventually melt, split into smaller liquid bits and then those would eventually vaporize, finally slowing down to not-quite-so-relativistic speeds.

One thing that's going to happen, every hydrogen atom, or God forbid, every larger atom or collection of atoms that hits this thing is going to provide kinetic energy that goes into it and heats it up. I'm assuming the hydrogen atom will be trapped within the sphere (that makes for 100 percent energy transfer into the sphere, making for easier calculation), but at that speed it may well go through, and maybe even take bits of iron nuclei with it.

At rest in empty space the temperature will stabilize at the 3k background radiation, and you can (ignoring heat lost to radiation, which would become significant over time) calculate the temperature rise from there using the energy input and the specific heat of iron. The total input per unit time is of course the number of hydrogen atoms in interstellar space within a cylinder that's the cross-section path of this thing that it travels through in that time.

For the energy of each strike you would calculate the kinetic energy of a hydrogen atom at .999c. With the Lorentz transformations it would be hundreds or maybe thousands of times the kinetic energy as calculated using Newtonian mechanics. At that speed I don't think it would make much difference (again, this is just my SWAG) if its an ordinary-matter hydrogen atom or an antimatter hydrogen atom, as the kinetic energy is so large.

Geez, I'm not up on my space opera, but I wonder what the heck that railgun is tied down to. Its design and where it gets that amount of energy are also intriguing questions (Perhaps it's powered by a nuckear explosion, something like the SDI's X-ray Laser), but for this post I'll put those on the back burner.

The reaction force would be huge. I could imagine it being mounted on the Moon and that firing it (especially thousands or millions of times in the same general direction) could cause a measurable change in the Moon's orbit. You couldn't fire this from a smaller platform unless you don't care where or how fast the platform ends up going.

I have to wonder how much will still be iron. The hydrogen atom is likely to be stopped or slowed down by hitting an iron nucleus, which will likely split into smaller elements, and perhaps knocking out particles at speeds high enough to split other iron nuclei (any particle physicist should be able to tell you better what will happen). This thing could end up as a soup of atoms below iron on the periodic table. And some nuclei might even fuse, making atoms heavier than iron as well.

ETA: Would something "reasonable" like 0.1 or 0.2c be fast enough?

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I don't think that the iron would melt, even though whatever it hit would have great energy, it wouldn't all that much, but I don't think that the energies would be high enough for much fusion. It would be radiating infrared as fast as it would be absorbing energy.

BillPatt said:

Han Solo: Fast ship? You've never heard of the Millennium Falcon?
Obi-Wan: Should I have?
Han Solo: It's the ship that made the Kessel Run in less than twelve parsecs.

My favorite science goof in a movie.

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Actually it's been explained as not a goof, although there's quite a bit of BS involved in the explanation.

http://starwars.wikia.com/wiki/Parsec

BillPatt said:

The ambivalence here is in the "how long" formulation. Typically it means duration, I meant it to mean distance. I apologize if it was not clear.

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Then mentioning the object's speed would sure be helpful.

I think the biggest problem is not if it will erode away, but, as was said above, what are you firing it from? If you fire it from the moon, the moon will be pushed in the opposite direction of about 75m/year!!!! The implications could be huge. Even if you fire them from Earth it will still move quite a bit. Not to mention that the force would have to be dispersed over the entire planet/moon for it not to send the actual gun hurling through the planet/moon

Another thought would be if you need it to go 2000ly, it will take 2000 years to reach it's target. This is one epic war if I do say so myself....

EDIT: I made a slight mishap in my moon calculation...Also, it will encounter over the course of it's 2000 year journey only about 93grams of hydrogen. .04g/year. Which would mean about 9x10^9 Joules of energy are absorbed by it per hour. Which is about the energy that a barrel of oil has. So I don't think it would melt, but it would get pretty warm...

Michael_T said:

I think the biggest problem is not if it will erode away, but, as was said above, what are you firing it from? If you fire it from the moon, the moon will be pushed in the opposite direction of about 3m/year!!!! If you're firing lots of these (or even just one) the implications could be huge. Even if you fire them from Earth it will still move quite a bit. Not to mention that the force would have to be dispersed over the entire planet/moon for it not to send the actual gun hurling through the planet/moon

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So it would be useful in ending global warming by shoving the Earth out to the orbit of Mars.

PeterL said:

So it would be useful in ending global warming by shoving the Earth out to the orbit of Mars.

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That is if you don't shoot your gun through the earth...

But no, the earth would be about 100 times slower in it's speed, so (according to my modified calculations) 75cm per year.

Michael_T said:

That is if you don't shoot your gun through the earth...

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That might be best for everyone.

But no, the earth would be about 100 times slower in it's speed, so (according to my modified calculations) 75cm per year.

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That depends on how the thing would be aimed. Would you mean orbital speed or speed of revolution? Both or either could be affected. Mounting the rail gun on an Equatorial mountain with an adjustable mount would that would allow one a 180 degree field in the vertical would allow one to really mess up the Earth's orbit.

Michael_T said:

I think the biggest problem is not if it will erode away, but, as was said above, what are you firing it from? If you fire it from the moon, the moon will be pushed in the opposite direction of about 75m/year!!!! The implications could be huge. Even if you fire them from Earth it will still move quite a bit. Not to mention that the force would have to be dispersed over the entire planet/moon for it not to send the actual gun hurling through the planet/moon

Another thought would be if you need it to go 2000ly, it will take 2000 years to reach it's target. This is one epic war if I do say so myself....

EDIT: I made a slight mishap in my moon calculation...Also, it will encounter over the course of it's 2000 year journey only about 93grams of hydrogen. .04g/year. Which would mean about 9x10^9 Joules of energy are absorbed by it per hour. Which is about the energy that a barrel of oil has. So I don't think it would melt, but it would get pretty warm...

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PeterL said:

That might be best for everyone.




That depends on how the thing would be aimed. Would you mean orbital speed or speed of revolution? Both or either could be affected. Mounting the rail gun on an Equatorial mountain with an adjustable mount would that would allow one a 180 degree field in the vertical would allow one to really mess up the Earth's orbit.

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Earth's orbit won't be the immediate concern - the recoil is going to have such a large force it will 1. implode the mountain it's mounted on (see the idea of distributing the force above), and 2. cause some big earthquakes. Even if it were somehow well distributed, it would move the Earth enough to cause some big ocean waves. I'm not considering Earth's internals.

I again say go with a more "reasonable" speed, about 0.2c, where the energies involved are orders of magnitude smaller than for 0.999c.

Actually firing it from earth (or any other planet with an atmosphere) would destroy that planet IMO. Even at non-relativistic speeds like .2c there would be so much friction that the heat would get (literally) astronomical. Every micro-second (one millionth of a second) the equilivlant of a 200 megaton nuke would go off (The biggest ever made was 40MT I believe).

Suffice to say you can't launch anything like that from a planet with an atmosphere.

Then too you have to consider the implications of how you are going to aim this thing....that would be impossible. (quantum mechanics would forbid the small scale adjustments you would need to make in order to hit something with a dumb missile 2000ly away) You would need on-board course correction.

Now if you were to say use a black hole (for acceleration) and a worm-hole (to "aim" and to hit the target in less than 60 generations) you could probably wave your hand enough to make me believe as I'm reading...

Willowmound said:

Then mentioning the object's speed would sure be helpful.

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Then, days later, he realised it was right there in the title all along.

How long does it take the interstellar medium to wear them away? I don't think it would. It would get hot, perhaps molten. But I don't think it would wear away significantly.
What are the energy consequences of them hitting a 1mm size dust grain? somewhere around 1x10^15 Joules (estimate, I didn't do the relativistic calculations). But that is like a .25 Megaton Nuke. (this assumes an inelastic collision) your missile is gone.
Would an astronomer using a telescope outside Earth's atmosphere be able to detect it by the light of it hitting interstellar hydrogen? Dust grains? Technically Yes, but since it's traveling so fast the light generated by it is barely out racing the iron. So the light from when it was first fired could reach earth, but then 2 years later the iron will hit. So if they can see the light from say 1ly away (A stretch because that's far, and a hot ball of iron would be VERY VERY VERY tough to see) they missile will hit about 8 hours later.
And what would that light look like? Cosmic rays? Incredibly blue-shifted infrared light? VERY blue shifted. Think cosmic rays.
And maybe that warming of the sphere, blue-shifted, would be visible? Technically yes, but look up at the sky one night. Alpha Centauri is a star and only 4ly away. Does it look like a blazing fireball? Then consider how much more energy that star has compared to your iron ball... Look at Mars or Venus... You would need a SUPER DUPER telescope pointed in just the right location. Also lets assume that you can see it at Venus range. Light takes about 3min or so to make it to Earth from there, so if you saw light from the ball at Venus, you would have .18 seconds before it would hit.

Basically what I'm saying is that a spec of dust would explode the ball. Detection is impossible (until it hits).

Every action has an equal and opposite reaction and Mass equals Energy divided by C squared.

The faster you fire a one metre sphere of iron, the more mass it has and that means the source will necessarily be pushed in the opposite direction.

Work out the mass at rest of this sphere and then ask yourself how much mass it will have at 0.99% of C.

Consider the length of your rail gun, the mass of whatever starship or moon or whatever, the railgun is mounted on and consider how much of a recoil that railgun and its platform will have to contend with and how sudden that recoil will be.

You're writing SciFi. You need to get the basic science right or think of some plausible way to side step issues like this.

Don't just ignore things like mass, recoil etc. Remember that mass increases with velocity and that it will be exponentially higher the closer you get to C.

BillPatt said:

As I explained above, I don't have to explain how it got to be fired, only that it did. The real story is the reaction on Earth to the threat.

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Yeah but the average scifi reader is going to pick holes in your science, thus preventing suspension of disbelief and leading to them not reading the novel.

An unfinished novel is a dissatisfied reader, a dissatisfied reader will not pick up another one of your books, no matter how much you improve.

And as pointed out, the reaction on Earth is going to be 'hmm I wonded what that off colour pixel on the display is'... KABOOM!!! The Earth explodes leaving a burned out mass of floating rubble in the habitable zone of a distant yellow star.